If Theymos himself banned you, you are pretty well screwed. If a Moderator bans you, an Admin can give the ban a second look using their own judgement. If their judgment banned you in the first place, you are probably done.
Well I don't know who banned me, but I assumed it was Theymos because the the e-mail address I was given to appel was contains @theymos.e4ward.com . Now that you mentioned could have been a moderator as well.
I deserved to be punished because I infringed a rule, however what really pissed me off is that no one gave me any explanation or answered my e-mails, and I apologized and ensured it would never happen again.
I did something wrong, but at least I recognized it and wanted to work on it.
Please keep that in mind and consider it. What do you say?
Theymos is the only one who can do ban appeals such as the contact info you were given when banned. It really depends on a variety of things as to how much warning you get. If you accidentally spam a bit, you will get your posts deleted and warned. If you spam 57 replies in an hour window, you aren't getting a warning. If your account was a newbie you are shown a tad less consideration than someone who has been around for 2 years and made a one time slip up.
Honestly, I'm glad that you recognize your mistake and did whatever you did to fix it, you get bonus points, but to be frank with you, if it was a global moderator that banned you unless there are extraordinary circumstances or it was a mistake that the moderator acknowledges, your chances at an appeal are realitively slim. If it was indeed Theymos himself, there is very little to no chance at an appeal.
Now while ban evasion is also against the rules and I wouldn't condone it (you are fine doing what you did making a new account to post here) if it really was a
small mistake that you have rectified, for a non serious offense, you are probably alright to just use your new account.